Editing the TTF file was the solution.
I've followed the suggestion from this answer and opened my TTF files on Glyphs and exported them again. Glyphs adjusted the ascender and lineGap values to something which is probably correct and the fonts behave pretty much identically on iOS 6 and IOS 7. The baseline now is even very close to the system fonts.
There are still some minor vertical differences, but apparently this happens with every font on iOS 7, even on system fonts, but it's much less noticeable.